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swat32
3 years ago
12

If f(x)=x^2+7, what is the equation for f^-1(x)???

Mathematics
2 answers:
Marrrta [24]3 years ago
5 0
Given: f(x) = x² + 7

Let  y = x² + 7
x = y² + 7 (since the inverse is reflected about the y = x line, the coordinates are interchangeable)

y² = x - 7
y = √(x - 7)

Thus, the inverse function f^(-1)x = √(x - 7)
PIT_PIT [208]3 years ago
4 0
So...
f(x)=x^2+7
Consider the output as being y.
y=x^2+7
Thinking of this as a step-by-step procedure (namely , take a number x , square it and then add 7 ) , to reverse this , we have to solve for x the equation y=x^2+7 .

y=x^2+7
x^2=y-7

x=\pm\sqrt{y-7}

\implies f^{-1}(x)=\pm\sqrt{y-7}

I think the answer is correct now...
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What interest rate, to the nearest tenth of a percent, that is required for an investment subject to continuous compounding to i
Sunny_sXe [5.5K]

Answer:

It will take an interest rate of 8.1% to get 150% of the initial investment in just 5 years.

Step-by-step explanation:

Use the formula for continuous compounding

X(t) = Pe^{rt}

where r stands for the (annual) interest rate, t for time in years, P for the initial principal (investment) and X is the amount after t years.

(this formula can be beautifully derived from just basic considerations, btw)

We are given t=5, and percent increase on the initial P, so we can solve for r

X(5) = 1.5P=Pe^{r\cdot5}\\1.5=e^{r\cdot5}\\\ln 1.5=\ln e ^{5r}\\\ln 1.5=5r\\r = \frac{\ln 1.5}{5}=0.081\rightarrow 8.1\%

It will take an interest rate of 8.1% to get 150% of the initial investment in just 5 years.

5 0
3 years ago
Two pieces of equipment were purchased for a total of $5000. If one piece cost $410 more than the other, find the price of the l
ankoles [38]

Answer:   i have never did a math problem like this before because i'm only in the 2nd semester of 7th grade but i will try, i think it is 2090

Step-by-step explanation: 5000 divided by 2 = 2500. then you do 2500-410. 2500-410= 2090.  (i hope this will help you and sorry if i did it wrong) :)

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2 years ago
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Step-by-step explanation:

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5 0
2 years ago
18x=36 with a full explanation and I will give you brainlyest
iris [78.8K]

Answer:−18x>36

Divide both sides by −18. Since −18 is negative, the inequality direction is changed.

x< −18

36

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Divide 36 by −18 to get −2.

x<−2

Step-by-step explanation:

Hope this helps!

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2 years ago
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divide total miles by time:

157.5 / 2.5 = 63 miles per hour

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3 years ago
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